SCALING LIMIT FOR A DRAINAGE NETWORK MODEL

We consider the two-dimensional version of a drainage network model introduced ill Gangopadhyay, Roy and Sarkar (2004), and show that the appropriately rescaled family of its paths converges in distribution to the Brownian web. We do so by verifying the convergence criteria proposed in Fontes, Isopi, Newman and Ravishankar (2002).

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

INFLUENCE OF ALTITUDE, AGE AND DIAMETER ON YIELD AND ALPHA-BISABOLOL CONTENT OF CANDEIA TREES (Eremanthus erythropappus)

The heartwood of candeia tree is a source of essential oil rich in alpha-bisabolol, a substance widely used in the cosmetic and pharmaceutical industry. Bearing in mind the economic importance of alpha-bisabolol, this work aimed to evaluate the influence of tree age on the yield and content of alpha-bisabolol present in essential oil from candeia, considering two distinct reliefs and three diameter classes, in Aiuruoca region, south Minas Gerais state. The two distinct reliefs correspond respectively to one section of the stand growing at 1,000m of altitude (Area 1) and another section growing at 1,100m of altitude (Area 2). In each section, 15 trees were felled from among 3 different diameter classes. Discs were removed from the base of each tree to estimate their age by doing growth ring count. Soil samples were taken and Subjected to physical and chemical analysis. The logs were reduced into chips and random samples were taken for distillation to extract essential oil. The method used was steam distillation at a pressure of 2 kgf/cm(2)/2.5 h. The chemical analysis was performed in a gas chromatograph (GC) based on the alpha-bisabolol standard reference. The yield of essential oil from trees in Area I was higher than that from trees in Area 2, with the same pattern of influence for older trees. In Area 2, the alpha-bisabolol content was higher in younger trees. No differences were found between the relevant parameters in relation to diameter classes.

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

BORON UPTAKE AND DISTRIBUTION IN FIELD GROWN CITRUS TREES

In low fertility tropical soils, boron (B) deficiency impairs fruit production. However, little information is available on the efficiency of nutrient application and use by trees. Therefore, this work verified the effects of soil and foliar applications of boron in a commercial citrus orchard. An experiment was conducted with fertigated 4-year-old `Valencia` sweet orange trees on `Swingle` citrumelo rootstock. Boron (isotopically-enriched 10B) was supplied to trees once or twice in the growing season, either dripped in the soil or sprayed on the leaves. Trees were sampled at different periods and separated into different parts for total B contents and 10B/11B isotope ratios analyses. Soil B applied via fertigation was more efficient than foliar application for the organs grown after the B fertilization. Recovery of labeled B by fruits was 21% for fertigation and 7% for foliar application. Residual effects of nutrient application in the grove were observed in the year after labeled fertilizer application, which greater proportions derived from the soil supply.

Allometric models for estimating the phytomass of a secondary Atlantic Forest area of southeastern Brazil

The purpose of this study was to develop and validate equations to estimate the aboveground phytomass of a 30 years old plot of Atlantic Forest. In two plots of 100 m², a total of 82 trees were cut down at ground level. For each tree, height and diameter were measured. Leaves and woody material were separated in order to determine their fresh weights in field conditions. Samples of each fraction were oven dried at 80 °C to constant weight to determine their dry weight. Tree data were divided into two random samples. One sample was used for the development of the regression equations, and the other for validation. The models were developed using single linear regression analysis, where the dependent variable was the dry mass, and the independent variables were height (h), diameter (d) and d²h. The validation was carried out using Pearson correlation coefficient, paired t-Student test and standard error of estimation. The best equations to estimate aboveground phytomass were: lnDW = -3.068+2.522lnd (r² = 0.91; s y/x = 0.67) and lnDW = -3.676+0.951ln d²h (r² = 0.94; s y/x = 0.56).

Synthesis and structural characterization of block and random low molecular weight copolymers composed of L-lactic acid and isosorbide succinate moieties

Isosorbide succinate moieties were incorporated into poly(L-lactide) (PLLA) backbone in order to obtain a new class of biodegradable polymer with enhanced properties. This paper describes the synthesis and characterization of four types of low molecular weight copolymers. Copolymer I was obtained from monomer mixtures of L-lactide, isosorbide, and succinic anhydride; II from oligo(L-lactide) (PLLA), isosorbide, and succinic anhydride; III from oligo(isosorbide succinate) (PIS) and L-lactide; and IV from transesterification reactions between PLLA and PIS. MALDI-TOFMS and 13C-NMR analyses gave evidence that co-oligomerization was successfully attained in all cases. The data suggested that the product I is a random co-oligomer and the products II-IV are block co-oligomers.

WOOD DENSITY VARIATION AND TREE RING DEMARCATION IN Gmelina arborea TREES USING X-RAY DENSITOMETRY

Due to its relationship with other properties, wood density is the main wood quality parameter. Modern, accurate methods - such as X-ray densitometry - are applied to determine the spatial distribution of density in wood sections and to evaluate wood quality. The objectives of this study were to determinate the influence of growing conditions on wood density variation and tree ring demarcation of gmelina trees from fast growing plantations in Costa Rica. The wood density was determined by X-ray densitometry method. Wood samples were cut from gmelina trees and were exposed to low X-rays. The radiographic films were developed and scanned using a 256 gray scale with 1000 dpi resolution and the wood density was determined by CRAD and CERD software. The results showed tree-ring boundaries were distinctly delimited in trees growing in site with rainfall lower than 25 10 mm/year. It was demonstrated that tree age, climatic conditions and management of plantation affects wood density and its variability. The specific effect of variables on wood density was quantified by for multiple regression method. It was determined that tree year explained 25.8% of the total variation of density and 19.9% were caused by climatic condition where the tree growing. Wood density was less affected by the intensity of forest management with 5.9% of total variation.

Variation in the wood anatomical structure of Gmelina arborea (Verbenaceae) trees at different ecological conditions in Costa Rica

The tree Gmelina arborea has been widely introduced in Costa Rica for commercial purposes. This new conditions for melina cause variations on anatomy in secondary xylem of the trees growing in plantations. The objective of the present research was to determine the variation in the anatomy of xylem caused by the ecological conduction variation. Dimensions of fiber, axial parenchyma percentage of cross sections, parameters of vessels and the ray were measured. The results showed that some anatomical characteristics remained stable despite variations of ecological conditions, especially radial parenchyma and anatomical features which were less affected by the altitude. On the other hand, the vessels, axial parenchyma and fiber were less stable because they were affected significantly by the longitude, latitude, altitude and precipitation. Latitude significantly affected vessel percentage, length and diameter of the fiber and lumen. Longitude affected vessel percentage and fiber diameter. Altitude had a significant correlation with the amount of cells at my height. Annual average precipitation affected vessel percentage and diameter, not only of the fiber, but also of the lumen. These results suggest that the new growth conditions of G. arborea trees in Costa Rica have produced an anatomic adaptation.

Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Effect of Low-Level Laser Therapy on Malondialdehyde Concentration in Random Cutaneous Flap Viability

Objective: The aim of this study was to assess the effects of 830 and 670 nm laser on malondialdehyde (MDA) concentration in random skin-flap survival. Background Data: Low-level laser therapy (LLLT) has been reported to be successful in stimulating the formation of new blood vessels and activating superoxide-dismutase delivery, thus helping the inhibition of free-radical action and consequently reducing necrosis. Materials and Methods: Thirty Wistar rats were used and divided into three groups, with 10 rats in each one. A random skin flap was raised on the dorsum of each animal. Group 1 was the control group; group 2 received 830 nm laser radiation; and group 3 was submitted to 670 nm laser radiation. The animals underwent laser therapy with 36 J/cm(2) energy density immediately after surgery and on the 4 days subsequent to surgery. The application site of the laser radiation was 1 point, 2.5 cm from the flap's cranial base. The percentage of the skin-flap necrosis area was calculated 7 days postoperative using the paper-template method, and a skin sample was collected immediately after as a way of determining the MDA concentration. Results: Statistically significant differences were found between the necrosis percentages, with higher values seen in group 1 compared with groups 2 and 3. Groups 2 and 3 did not present statistically significant differences (p > 0.05). Group 3 had a lower concentration of MDA values compared to the control group (p < 0.05). Conclusion: LLLT was effective in increasing the random skin-flap viability in rats, and the 670 nm laser was efficient in reducing the MDA concentration.

Multi-trait and random regression mature weight heritability and breeding value estimates in Nelore cattle

Mature weight breeding values were estimated using a multi-trait animal model (MM) and a random regression animal model (RRM). Data consisted of 82 064 weight records from 8 145 animals, recorded from birth to eight years of age. Weights at standard ages were considered in the MM. All models included contemporary groups as fixed effects, and age of dam (linear and quadratic effects) and animal age as covariates. In the RRM, mean trends were modelled through a cubic regression on orthogonal polynomials of animal age and genetic maternal and direct and maternal permanent environmental effects were also included as random. Legendre polynomials of orders 4, 3, 6 and 3 were used for animal and maternal genetic and permanent environmental effects, respectively, considering five classes of residual variances. Mature weight (five years) direct heritability estimates were 0.35 (MM) and 0.38 (RRM). Rank correlation between sires' breeding values estimated by MM and RRM was 0.82. However, selecting the top 2% (12) or 10% (62) of the young sires based on the MM predicted breeding values, respectively 71% and 80% of the same sires would be selected if RRM estimates were used instead. The RRM modelled the changes in the (co) variances with age adequately and larger breeding value accuracies can be expected using this model.

Spatial patterns in the brood combs of Nannotrigona testaceicornis (Hymenoptera: Meliponinae): male clusters

Genetic models of sex and caste determination in eusocial stingless bees suggest specific patterns of male, worker and gyne cell distribution in the brood comb. Conflict between queen and laying workers over male parentage and center-periphery gradients of conditions, such as food and temperature, could also contribute to non-random spatial configuration. We converted the positions of the hexagonal cells in a brood comb to Cartesian coordinates, labeled by sex or caste of the individuals inside. To detect and locate clustered patterns, the mapped brood combs were evaluated by indexes of dispersion (MMC, mean distance of cells of a given category from their centroid) and eccentricity (DMB, distance between this centroid and the overall brood comb centroid) that we developed. After randomizing the labels and recalculating the indexes, we calculated probabilities that the original values had been generated by chance. We created sets of binary brood combs in which males were aggregated, regularly or randomly distributed among females. These stylized maps were used to describe the power of MMC and DMB, and they were applied to evaluate the male distribution in the sampled Nannotrigona testaceicornis brood combs. MMC was very sensitive to slight deviations from a perfectly rounded clump; DMB detected any asymmetry in the location of these compact to fuzzy clusters. Six of the 82 brood combs of N. testaceicornis that we analyzed had more than nine males, distributed according to variations in spatial patterns, as indicated by the two indexes.

Random X Inactivation and Extensive Mosaicism in Human Placenta Revealed by Analysis of Allele-Specific Gene Expression along the X Chromosome

Imprinted inactivation of the paternal X chromosome in marsupials is the primordial mechanism of dosage compensation for X-linked genes between females and males in Therians. In Eutherian mammals, X chromosome inactivation (XCI) evolved into a random process in cells from the embryo proper, where either the maternal or paternal X can be inactivated. However, species like mouse and bovine maintained imprinted XCI exclusively in extraembryonic tissues. The existence of imprinted XCI in humans remains controversial, with studies based on the analyses of only one or two X-linked genes in different extraembryonic tissues. Here we readdress this issue in human term placenta by performing a robust analysis of allele-specific expression of 22 X-linked genes, including XIST, using 27 SNPs in transcribed regions. We show that XCI is random in human placenta, and that this organ is arranged in relatively large patches of cells with either maternal or paternal inactive X. In addition, this analysis indicated heterogeneous maintenance of gene silencing along the inactive X, which combined with the extensive mosaicism found in placenta, can explain the lack of agreement among previous studies. Our results illustrate the differences of XCI mechanism between humans and mice, and highlight the importance of addressing the issue of imprinted XCI in other species in order to understand the evolution of dosage compensation in placental mammals.